Well, if the USS Rhode Island is being fired upon by Klingons in ST: Voyager Endgame, then its a pretty safe bet that there are tension running high between the Feds and the Klingons (as clearly outlined in STO). And no matter how nice the Romulans may seem, they're always going to have a trick up their sleeve. Cardassia is in ruins. The Gamma quadrant has barely been explored, who knows what enemies might turn up? The Dominion could just sit back and relax, maybe poke the Feds a bit.
And that's all 25th Century.
Problems with a TMP era series is that if there is a noted key member (like a Picard family member), they're going to have to live long enough to do the key things seen in later series. The only way to have a completely free series is to have a new ship, new crew, new areas to explore. I like the idea of Romulan TMP ships though since all the TMP films focused mainly on the Klingons.